平面三角形

All meshing elements except those are adjacent to edge and transition elements are equilateral triangle, which is very useful for finite element computation.

提出了一种可在平面内进行三角形有限元网格划分的方法，该方法可以在任意二维区域进行剖分；剖分单元除了边界和部分过度单元外，主要为等边三角形。

Baptistery is located in the west of the church, flat triangle, diameter 274 m.

洗礼堂位于教堂以西，平面三角形，直径274米。

The result showed that the value of the binding energy was in reasonable agreement with available experimental data, as well as with other theoretical results, and the most stable structure was the triangle of plane.

对所得异构体的结合能和结构进行了分析，发现结合能和实验值以及理论值符合得很好，在结构方面其最稳定的是平面三角形结构。

Various methods such as the relationship of area, and the distance of the triangle to the centralness of three dots, the distance from the interior point, exterior point, the barycenter to the vertices of triangle, and the standard error and differences average obtained from three dots were determined with a dynamic geometry software GSP, and a statistic method was used to find a least error way to determine the centralness of three dots on a plane.

本研究是以平面上三点所构成的三角形之三顶点做讨论，分别以三角形的面积、周长，内心、外心和重心至三顶点距离，三点的标准差及平均差的概念，做为不同的判别方式，并以动态几何画板 GSP模拟不同的判断方法作为研究，再利用统计学上的方法，找出哪一种定义方式为最适合、误差最少的判断方法。

It was proved that the area coordinates of plane triangle element and the volume coordinates of tetrahedron element are equivalent to the oblique Cartesian coordinates by the analytical and geometrical methods.

本文通过分析法和几何法证明：在有限元法和边界元法中，平面三角形单元的面积坐标或四面体单元的体积坐标与由这些单元的二边或三边构成的斜交笛卡儿二维坐标或三维坐标，尽管定义不同，而其内容却是完全对等的。

A plane to the triangle, triangle identified include this in two parallel axes of the smallest rectangle.

給一個平面上的三角形，找出包含此三角形且平行於兩軸的最小矩形。

The formula for area of ellipsoidal triangle on earth ellipsoid by means of geodesic coordinate is derived in this paper. It is showed that the primary term is identical with the formula for area of plane triangle by planimetric rectangular coordinate in three angular point, while the expression of remainder terms has also regularity of its form. The presented formula can be applicable also to convex polygon on earth ellipsoid.

本文推导出用三顶点的测地坐标计算地球椭球面上三角形面积的公式，公式表明，其主项的表示式与按平面坐标求面积的计算式完全一致，而附加项的表示式亦有规律可循，因此该公式的适用范围可由椭球面三角形推广至椭球面上任意凸多边形。

From calculating the maximum distance between the vertexes and their related average plane for each triangle, and based on the triangle area, surface attribute and the predefined characteristics, the algorithm gives out the triangle's weight, the collapse orders of triangle and makes a continuous level of detail model.

算法计算三角形顶点到相关平均平面的距离的最大值，结合三角形的面积、表面属性和预设特征给出三角形权值，确定折叠次序；并能够用累进网格实现连续的层次细节模型。

For a given ray and a complex scene including dense triangle meshes, this approach can cull most nonintersecting triangles by a simple rejection test that only involves triangle/plane intersection tests.

针对由稠密三角形网格组成的复杂场景，算法通过三角形和测试平面的相交判断剔除与投射光线不相交的绝大多数三角面片。

The special geometric restrictions like parallelism andperpendicularity implicated in vanishing elements are deeply studied. In single-view case,the theory is presented to interpret relationship between two planar lines by applying 3Dinvariants of vanishing points. In two-view case, the method on extraction vanishing pointof an arbitrary spatial line is described, and moreover, the theory is presented to interpretrelationship between two elements in 3D space, such as two lines, two planes, line andplane, and so on.

4详细论述了消失元素(消失点、消失直线、消失平面等)所体现的垂直、平行等特殊几何约束关系；对单视图，提出了一种利用消失点列的3D不变量解释平面直线关系的方法；对双视图，提出了利用自共轭三角形和对极几何约束，提取任意直线的消失点的算法，并在此基础了提出了一种利用消失元素的3D不变量解释直线间、直线与平面间、平面间等多种空间几何关系的方法。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。